Something obviously isn't working correctly, perhaps a poor connection somewhere on the battery wiring or even a Hall Sensor wire or Phase wire connection within the controller itself.
I would suggest removing the internal controller and checking the Hall Sensor and Phase wire connections to ensure everything is properly connected. Make sure that none of the pins/sockets in the Hall Sensor connector have been pushed out the rear of the connector during insertion.
If you cannot find an obvious fault, it could possibly be that the controller itself is causing the stuttering.
It is unlikely to be your battery voltage causing the problem as the MPIII controllers can handle actual voltages from ~20V up to 60V maximum
(Please note that it will not work with a nominal 60V battery, which is much too high, as it would be nearer to 70V when fully charged).
Unlike the MP4 and MP5 Vector controllers, the MPIII square wave controllers used to run on 24V, 36V or 48V batteries regardless of the voltage setting in the programming software.
Before I replaced it with a MP4, I regularly used my MPIII on both 7S and 14S lithium packs on the 24V setting without a problem.
The typical battery current draw with a MPIII controller was 25~30A maximum, which is why I suggested setting your CA current setting to 25A.
Alan